Geometrical Optics Fiber optics The eye

Transcription

1 Phys 322 Lecture 16 Chapter 5 Geometrical Optics Fiber optics The eye

2 First optical communication Alexander Graham Bell : photophone 4 years after inventing a telephone!

3 Fiberoptics: first lightguide 1870: water as a light guide John Tyndall

4 Propagation of light in an optical fiber Light travels through the core bouncing from the reflective walls. The walls absorb very little light from the core allowing the light wave to travel large distances. Some signal degradation occurs due to imperfectly constructed glass used in the cable. The best optical fibers show very little light loss -- less than 5%/km at 1,550 nm. Maximum light loss occurs at the points of maximum curvature.

5 Fiber optics: communications 1960: First laser 1966: coupling with fibers for communication 1970: 1% of light transmitted over 1 km (losses 20 db/km) Today: over 96% of power transmitted over 1 km Why light? - frequencies ~10 15 Hz Theoretical bandwidth limit: each oscillation is 1 bit, bandwidth is ~10 14 bytes/second (100,000 GB/s) Speech ~3 kb/s: can support ~10 billion phone connections over one fiber simultaneously! DVD quality videophone: ~10 million channels! Note: Modern fiber systems record 100 Tb/s

6 What is an Optical Fiber? An optical fiber is a waveguide for light consists of : core cladding buffer jacket inner part where wave propagates outer part used to keep wave in core protective coating outer protective shield

7 Design of optical fibers Core: Thin glass center of the fiber that carries the light Cladding: Surrounds the core and reflects the light back into the core Buffer coating: Plastic protective coating n core > n cladding

8 Microstructure fiber In microstructure fiber, air holes act as the cladding surrounding a glass core. Such fibers have different dispersion properties. Air holes Core Such fiber has many applications, from medical imaging to optical clocks.

9 Step Index Fiber: TIR escapes core cladding n t escapes core core n i i stuck in core i i For total internal reflection need n c <n f sin n t n c ti n i c for TIR i critical angle (pg 122)

10 Critical Bend radius

11 Fiberoptics: single core fiber losses Consider large fiber: diameter D >> can use geometric optics Path length traveled by ray: l L / cos Number of reflections: l N 1 D / sin t t Example: L = 1 km, D = 50 m, n f =1.6, i = 30 o N = 6,580,000 Note: frustrated internal reflection, irregularities losses! Using Snell s Law for t : N D Lsin n 2 f i sin 2 1 i

12 Numerical Aperture A measure of a lens size is the numerical aperture. It s the product of the medium refractive index and the marginal ray angle. NA = n sin() f Why this definition? Because the magnification can be shown to be the ratio of the NA on the two sides of the lens. High-numerical-aperture lenses are bigger.

13 Numerical Aperture NA n sin describes light gathering capability for: lenses microscope objectives (where n may not be 1) optical fibers NA photons gathered

14 Numerical aperture (NA) of a n i Step Index Fiber n c n f t 90- t Cladding - transparent layer core of a fiber (reduces losses and f/#) max must be > critical angle NA n outside sin max NA step n f 2 n i n 2 c NA step n f 2 n 2 c NA in air

15 Fiber and f/# sin max n 2 f n i n 2 c Angle max defines the light gathering efficiency of the fiber, or numerical aperture NA: NA n i sin max n 2 f n 2 c And f/# is: 2NA f /# 1 Largest NA=1 Typical NA = 0.2 1

16 Bundles Coherent bundles: flexible image carriers Bundles can collect light from larger area and be still flexible Flexible light carriers Fibers are arranged in a coherent fashion

17 Data transfer limitations 1. Distance is limited by losses in a fiber. Losses are measured in decibels (db) per km of fiber (db/km), i.e. in logarithmic scale: 10 L log Po P i Po P Example: P o /P i over 1 km 10 db 1:10 20 db 1: db 1:1000 i 10 L /10 P o - output power P i - input power L - fiber length Workaround: use light amplifiers to boost and relay the signal 2. Bandwidth is limited by pulse broadening in fiber and processing electronics

18 Attenuation Rayleigh Scattering page 297 IR absorption absorption and scattering in fiber in the IR: low-oh versus high-oh (lower optimal wavelength)

19 Pulse broadening Dispersion: The Basics Light propagates at a finite speed fastest ray slowest ray fastest ray: one traveling down middle ( axial mode ) slowest ray: one entering at highest angle ( high order mode) will be a difference in time for these two rays

20 Effect of Dispersion initial pulse farther down farther still time time time modal example: step index ~ 24 ns km -1 GRIN ~ 122 ps km -1

21 Types of Dispersion in Fibers modal material waveguide non-linear time delay from path length differences usually the biggest culprit in step-index n() : different times to cross fiber (note: smallest effect ~ 1.3 m) changes in field distribution (important for SM) n can become intensity-dependent NOTE: GRIN fibers tend to have less modal dispersion because the ray paths are shorter

22 Pulse broadening Multimode fiber: there are many rays (modes) with different OPLs and initially short pulses will be broadened (intermodal dispersion) For ray along axis: t min L v f Ln 2 For ray entering at max : t l v Ln cn max The initially short pulse will be broadened by: Making n c close to n f reduces the effect! Ln f n f t tmax tmin 1 c nc f f f c c

23 Pulse broadening: example n f = 1.5 n c =1.489 Estimate the bandwidth limit for 1000 km transmission. Solution: Ln f t c n n f c s Even the shortest pulse will become ~37 s long Bandwidth ~ s 27 kbps Multimode fibers are not used for communication! 5 s 37s kilobits per second = ONLY 3.3 kbytes/s

24 Fibers carry modes of light number of modes D 0 NA 2 a mode is : a solution to the wave equation a given path/distribution of light (pg 196) higher # modes gives more light, which is not always desirable

25 Example of # of 850nm Silica step-index fiber has n f = 1.452, n c = (NA = 0.205) SELFOC graded index fiber with same NA diameter (microns) # step-index modes # GRIN modes E3 37 E3 230 E E3 46 E E3 high # modes implies classical optics

26 NA and # of Modes killed ray propagated ray large NA small NA

27 Graded Index Fiber n c n varies quadratically n f n c like a restoring force!

28 Types of fibers n c n c n f n c n c n f n c n c n f GRIN step-index singlemode step-index multimode

29 Single mode fiber To avoid broadening need to have only one path, or mode Single mode fiber: there is only one path, all other rays escape from the fiber clad core jacket Geometric optics does not work anymore: need wave optics. Single mode fiber core is usually only 2-7 micron in diameter

30 Single mode fiber: broadening clad core jacket Transform limited pulse product of spectral full width at half maximum (fwhm) by time duration fwhm: ft 0.2 Problem: shorter the pulse, broader the spectrum. refraction index depends on wavelength A 10 fs pulse at 800 nm is ~40 nm wide spectrally If second derivative of n is not zero this pulse will broaden in fiber rapidly Solitons: special pulse shapes that do not change while propagating

31 An example: I need a fiber that will conduct NIR light. I have to keep a tight pulse pattern. It must couple into an LED. What do I do?

32 Putting It All together (a) I needed a fiber that will conduct NIR light. get a low OH fiber (b) I had to keep a tight pulse pattern. you want low dispersion: SM or a GRIN fiber, low diameter, low NA (c) It must couple into an LED. The LED has a high divergence angle; better get a bright one. A laser might be better, and use a GRIN lens to couple. These are design considerations, as well as cost!

33 Light: wavelength and color Typically light is a mixture of EM waves at many frequencies: E net Ei E0i cos it ki r i i i Power of waves of each wavelength forms a spectrum of EM radiation I() Sun spectrum: Mixture of all wavelengths is perceived by people as white light. How do we see colors?

34 Scattering and color Water is transparent, vapor is white: diffuse reflection from droplets White paint: suspension of colorless particles (titanium oxide etc.) Scattering depends on difference in n between substances: wet surfaces appear darker - less scattering Oily paper - scatters less

35 The Eyeball There are four kind of detectors of light. They are built around four kinds of organic molecules that can absorb light of different wavelength Color vision - three kinds of cones, B&W - rods

36 The eye s response to light and color The eye s cones have three receptors, one for red, another for green, and a third for blue.

37 The Eye: a digital camera? Brain interprets each combination of three signals from R, G and B receptors (cones) as a unique color There are ~120 million receptors in your eye Equivalent to 120 Megapixel digital camera! Signal color R G B red yellow green blue

38 The eye is poor at distinguishing spectra. Because the eye perceives intermediate colors, such as orange and yellow, by comparing relative responses of two or more different receptors, the eye cannot distinguish between many spectra. The various yellow spectra below appear the same (yellow), and the combination of red and green also looks yellow!

39 RGB vision Suppose we think that light is yellow. What wavelength is it? R G B yellow Is = 560 nm? Lets mix two light waves at 650 nm and 530 nm in proportion 1.9:0.73 R= It will be indistinguishable G= from yellow!

40 RGB: additive coloration By mixing three wavelengths we can reproduce any color! Primary colors for additive mixing: Red, Green, Blue Complimentary colors - magenta, cyan, yellow (one of the primaries is missing)

41 Computer monitors LCD display

42 How film and digital cameras work

43 Most digital cameras interleave different-color filters

44 CMY: subtractive coloration Use white light and absorb some spectral components Primary colors for additive mixing: Cyan, Magenta, Yellow Cyan - absorbs red Yellow - absorbs blue Magenta - absorbs green Any picture that is to be seen in ambient white light can be painted using these three colors. Color printer: uses CMYK - last letter stands for Black (for better B&W printing) Dyes: molecules that absorb light at certain wavelengths in visible spectral range (due to electronic transitions)